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Proof step 2 from proof pot2-le-pred (previous step)

2 ^ i < 2 ^ (i - 1) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 4:
¬ 0 < i, 2 ^ i < 2 ^ (i - 1) ⊦

Rule argument

spec: int-pot inst: name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [i, 2] flags: rewrite, current

Additional information

Used simplifier rules: two-lsz: ⊦ ¬ 2 ^ i < 0;%sub-pred: ⊦ i -1 = i - 1; from specification int-abs%numls-07: ⊦ (* i1) * j < j ↔ 0 < (1 - i1) * j; from specification int-mult%minus-one-02: ⊦ ~1 * i = ~ i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%neg: ⊦ 0 < ~ i ↔ i < 0; from specification int-abs Used terms: i, 2